/*
For every $n \ge 1$ the prime-counting function $\pi(n)$ is equal to the number of primes
not exceeding $n$.
E.g. $\pi(6)=3$ and $\pi(100)=25$.


We say that a sequence of integers $u  = (u_0,\cdots,u_m)$ is a $\pi$ sequence if 
 $u_n \ge 1$ for every $n$
 $u_{n+1}= \pi(u_n)$
 $u$ has two or more elements

For $u_0=10$ there are three distinct $\pi$ sequences: (10,4),  (10,4,2) and (10,4,2,1).


Let  $c(u)$ be the number of elements of $u$ that are not prime.
Let $p(n,k)$ be the number of $\pi$ sequences $u$  for which $u_0\le n$ and $c(u)=k$.
Let $P(n)$ be the product of all $p(n,k)$ that are larger than 0.
You are given: P(10)=3×8×9×3=648 and P(100)=31038676032.


Find $P(10^8)$. Give your answer modulo 1000000007.

Anser:
Time:
*/
package main

import (
	"fmt"
	"time"
)

func main() {
	tstart := time.Now()



	tend := time.Now()
	fmt.Println(tend.Sub(tstart))
}